Last week, before all this fractal nonsense, I had a post about real valued functions of the plane, viewed as images. I figure that since I am short on time, it would be neat to have a post about why viewing these as images rather than as the graphs of multivariable calculus is “good”. Put another way, why should we sometimes draw a square and color each pixel a different shade of gray depending on the value of the function at that pixel, rather than represent these “intensities” of gray as heights.
As a warning, some of the “graphs” of images actually look pretty cool, and the MATLAB coloring algorithm apparently works hard to make sure nothing looks too bad. In particular, you can adjust the view on any of the graphs to get back pretty much the picture you started with. But less commentary, more images. Also, this is an experiment- the images below are in a “gallery”, and clicking on them will make them much bigger: